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Sign-changing solutions for modified Schrödinger–Poisson system with general nonlinearity
Complex Variables and Elliptic Equations ( IF 0.9 ) Pub Date : 2021-07-01 , DOI: 10.1080/17476933.2021.1947258
Xueqin Peng 1 , Gao Jia 1 , Chen Huang 2
Affiliation  

This paper is concerned with the existence and multiplicity of sign-changing solutions for the following modified Schrödinger–Poisson system: Δu+V(x)u+κϕu12uu2=f(u),xR3,ϕ=u2,xR3, where κ(0,1),V(x) is coercive, the nonlinear term f is 4-superlinear at infinity but does not need any increasing condition. By using the method of invariant sets of descending flow, the existence and multiplicity of sign-changing solutions are obtained. Furthermore, we consider the asymptotical behavior of solutions with respect to the parameter κ. These results extend and complement some existing ones in the literature.



中文翻译:

具有一般非线性的修正薛定谔-泊松系统的符号转换解

本文关注以下修正薛定谔-泊松系统的符号变化解的存在性和多样性:-Δ+(X)+κφ-122=F(),XR3,-φ=2,XR3,在哪里κ(0,1),(X)是强制性的,非线性项f在无穷大处是 4-超线性,但不需要任何递增条件。利用递减流不变集的方法,得到了变号解的存在性和多重性。此外,我们考虑关于参数κ的解的渐近行为。这些结果扩展和补充了文献中的一些现有结果。

更新日期:2021-07-01
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